Definition:Special Linear Group
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Definition
Let $R$ be a commutative ring with unity whose zero is $0$ and unity is $1$.
The special linear group of order $n$ on $R$ is the set of square matrices of order $n$ whose determinant is $1$.
It is a group under (conventional) matrix multiplication.
It is denoted $\SL {n, R}$, or $\SL n$ if the ring is implicit.
The ring itself is usually a standard number field, but can be any commutative ring with unity.
Also known as
Some authors prefer $\operatorname{SL}_n \paren R$ and $\operatorname{SL}_n$ over $\SL {n, R}$.
Also see
- Results about the special linear group can be found here.
Sources
- 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 36$. Subgroups
